# subspaces of R^3 are lines and planes through the origin

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Determine which subsets given below are subspace of R^3

1) {x l x_1 greater or equal to 0}

2) {x l x_1=0}

3) {x l x_1+x_2+x_3=1}

4) {x l x_1+x_2+x_3=0}

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##### Solution Summary

This tutorial expresses how subspaces of R^3 are lines and planes through the origin.

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In general, subspaces of R^3 are lines and planes through the origin.

1) {x l x_1 greater or equal to 0}

This is not a subspace because it is not closed under additive inverses. For instance, (1,0,0) is in the set but (-1,0,0) is not.

2) {x l x_1=0}

This is ...

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